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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 67270v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67270.f2 | 67270v1 | \([1, 0, 1, -2423, 2234778]\) | \(-1771561/2430400\) | \(-2156988946302400\) | \([2]\) | \(368640\) | \(1.6213\) | \(\Gamma_0(N)\)-optimal |
| 67270.f1 | 67270v2 | \([1, 0, 1, -271503, 53790506]\) | \(2493877677481/33635000\) | \(29851186310435000\) | \([2]\) | \(737280\) | \(1.9679\) |
Rank
sage: E.rank()
The elliptic curves in class 67270v have rank \(0\).
Complex multiplication
The elliptic curves in class 67270v do not have complex multiplication.Modular form 67270.2.a.v
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
